Abstract
The relationship between Braid Theory and the organisation of periodic orbits of dynamical systems is considered.
It is shown that for some (physically relevant) 3-d flows the characterisation of periodic orbits by means of Braid Theory can be done on the Poincaré surface in an efficient way. The result is a thread-less graphical presentation of a braid class.
We discuss extensions of this approach to (adequate) dynamical systems of dimension higher than three, using results from Central Manifold Theory.
It is shown that for some (physically relevant) 3-d flows the characterisation of periodic orbits by means of Braid Theory can be done on the Poincaré surface in an efficient way. The result is a thread-less graphical presentation of a braid class.
We discuss extensions of this approach to (adequate) dynamical systems of dimension higher than three, using results from Central Manifold Theory.
| Original language | English |
|---|---|
| Pages (from-to) | 511-529 |
| Journal | Journal of Knot Theory and its Ramifications |
| Volume | 3 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 1994 |
Subject classification (UKÄ)
- Mathematical Sciences